Within 4 months of the ongoing COVID-19 pandemic caused by SARS-CoV-2, more than 250 nucleotide mutations have been detected in ORF1ab of the virus isolated from infected persons from different parts of the globe. These observations open up an obvious question about the rate and direction of mutational pressure for further vaccine and therapeutics designing. In this study, we did a comparative analysis of ORF1a and ORF1b by using the first isolate (Wuhan strain) as the parent sequence. We observed that most of the nucleotide mutations are C to U transitions. The rate of synonymous C to U transitions is significantly higher than the rate of non-synonymous ones, indicating negative selection on amino acid substitutions. Further, trends in nucleotide usage bias have been investigated in 49 coronaviruses species. A strong bias in nucleotide usage in fourfold degenerate sites toward uracil residues is seen in ORF1ab of all the studied coronaviruses: both in the ORF1a and in the ORF1b translated thanks to the programmed ribosomal frameshifting that has an efficiency of 14 – 45% in different species. A more substantial mutational U-pressure is observed in ORF1a than in ORF1b perhaps because ORF1a is translated more frequently than ORF1b. Mutational U-pressure is there even in ORFs that are not translated from genomic RNA plus strands, but the bias is weaker than in ORF1ab. Unlike other nucleotide mutations, mutational U-pressure caused by cytosine deamination, mostly occurring during the RNA plus strand replication and also translation, cannot be corrected by the proof-reading machinery of coronaviruses. The knowledge generated on the mutational U-pressure that becomes stronger during translation of viral RNA plus strands has implications for vaccine and nucleoside analog development for treating COVID-19 and other coronavirus infections.